Problem: Solve for $x$ : $2x^2 - 14x + 24 = 0$
Dividing both sides by $2$ gives: $ x^2 {-7}x + {12} = 0 $ The coefficient on the $x$ term is $-7$ and the constant term is $12$ , so we need to find two numbers that add up to $-7$ and multiply to $12$ The two numbers $-4$ and $-3$ satisfy both conditions: $ {-4} + {-3} = {-7} $ $ {-4} \times {-3} = {12} $ $(x {-4}) (x {-3}) = 0$ Since the following equation is true we know that one or both quantities must equal zero. $(x -4) (x -3) = 0$ $x - 4 = 0$ or $x - 3 = 0$ Thus, $x = 4$ and $x = 3$ are the solutions.